There are different types of these devices; the main differences are price, and the type of battery that provides the power. There are pretty low-cost external devices that use AA batteries, and there are also batteries like the Quantum Battery products, which use sealed, rechargeable batteries inside them, like say, sealed lead-acid type batteries. The first type, the one using AA batteries, is an e-Bay-era staple, and can be bought fairly cheaply. The genuine Quantum brand batteries cost more, but provide higher performance.
You need to make sure whatever you buy will actually "fit" or "hook up to" your specific flash model or models. Some devices use a cord that plugs in to a small port on the flash; other devices use a cord that has a large module on the end which goes into the actually battery compartment on the flash unit, and may require modifying the door on the flash.
Shots per charge depends on several factors: battery storage capacity, ambient temperature, and the speed of the flashes being fired, and the flash power used. For example, firing full-power flashes once every 14 seconds might net you only say, 400 flashes, but firing AUTO-mode flashes with the camera at ISO 640 and the lens aperture set to f/4.8 might provide 1,500 flashes. Similarly, long delays between flashes tend to exhaust a battery much less quickly than when the battery is used to power the flash very rapidly, over long stretches of firing.